If f(x)={((sin(1+[x]))/([x])"for"[x] ne ...

If `f(x)={((sin(1+[x]))/([x])"for"[x] ne 0,),(0" for " [x]-0,):}` where `[x]` denotes the greatest integer not exceeding x, then `lim_(xto0^-)f(x)=`

A

-1

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:

B

We have,
`f(x)={((sin(1+[x]))/(underset(0)[[x]])"for"x notin0,1),(0" for " xnotin,[0,1)):}`
`because lim_(xto0^-)f(x)=lim_(xto 0^-)(sin(1+[x]))/([x])=lim_(xto0^-)(sin(1-1))/(-1)=(0)/(-1)=0`

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